LMFDB - Embedded newform 8027.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72223 q^{2} +2.61290 q^{3} +5.41054 q^{4} -3.36664 q^{5} -7.11292 q^{6} -3.38304 q^{7} -9.28427 q^{8} +3.82726 q^{9} +O(q^{10})$	\(q-2.72223 q^{2} +2.61290 q^{3} +5.41054 q^{4} -3.36664 q^{5} -7.11292 q^{6} -3.38304 q^{7} -9.28427 q^{8} +3.82726 q^{9} +9.16478 q^{10} +1.99769 q^{11} +14.1372 q^{12} -5.35442 q^{13} +9.20942 q^{14} -8.79672 q^{15} +14.4528 q^{16} +1.58589 q^{17} -10.4187 q^{18} +5.90174 q^{19} -18.2154 q^{20} -8.83957 q^{21} -5.43817 q^{22} +1.00000 q^{23} -24.2589 q^{24} +6.33429 q^{25} +14.5760 q^{26} +2.16156 q^{27} -18.3041 q^{28} +2.91547 q^{29} +23.9467 q^{30} -6.92307 q^{31} -20.7754 q^{32} +5.21977 q^{33} -4.31716 q^{34} +11.3895 q^{35} +20.7076 q^{36} +1.21509 q^{37} -16.0659 q^{38} -13.9906 q^{39} +31.2568 q^{40} +8.92006 q^{41} +24.0633 q^{42} +3.74678 q^{43} +10.8086 q^{44} -12.8850 q^{45} -2.72223 q^{46} -6.58370 q^{47} +37.7639 q^{48} +4.44498 q^{49} -17.2434 q^{50} +4.14378 q^{51} -28.9703 q^{52} +6.93088 q^{53} -5.88426 q^{54} -6.72551 q^{55} +31.4091 q^{56} +15.4207 q^{57} -7.93658 q^{58} +10.3769 q^{59} -47.5950 q^{60} -6.67661 q^{61} +18.8462 q^{62} -12.9478 q^{63} +27.6498 q^{64} +18.0264 q^{65} -14.2094 q^{66} -13.5866 q^{67} +8.58053 q^{68} +2.61290 q^{69} -31.0049 q^{70} +1.16563 q^{71} -35.5333 q^{72} +6.20236 q^{73} -3.30776 q^{74} +16.5509 q^{75} +31.9316 q^{76} -6.75827 q^{77} +38.0856 q^{78} -6.89733 q^{79} -48.6576 q^{80} -5.83385 q^{81} -24.2825 q^{82} -5.22799 q^{83} -47.8268 q^{84} -5.33913 q^{85} -10.1996 q^{86} +7.61784 q^{87} -18.5471 q^{88} -9.89423 q^{89} +35.0760 q^{90} +18.1142 q^{91} +5.41054 q^{92} -18.0893 q^{93} +17.9224 q^{94} -19.8691 q^{95} -54.2842 q^{96} +3.59806 q^{97} -12.1003 q^{98} +7.64569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.72223	−1.92491	−0.962454	−	0.271446i	$-0.912498\pi$
$2$	−2.72223	−1.92491	−0.962454	+	0.271446i	$0.912498\pi$
$3$	2.61290	1.50856	0.754280	−	0.656553i	$-0.227986\pi$
$3$	2.61290	1.50856	0.754280	+	0.656553i	$0.227986\pi$
$4$	5.41054	2.70527
$5$	−3.36664	−1.50561	−0.752805	−	0.658244i	$-0.771299\pi$
$5$	−3.36664	−1.50561	−0.752805	+	0.658244i	$0.771299\pi$
$6$	−7.11292	−2.90384
$7$	−3.38304	−1.27867	−0.639335	−	0.768928i	$-0.720790\pi$
$7$	−3.38304	−1.27867	−0.639335	+	0.768928i	$0.720790\pi$
$8$	−9.28427	−3.28248
$9$	3.82726	1.27575
$10$	9.16478	2.89816
$11$	1.99769	0.602326	0.301163	−	0.953573i	$-0.402625\pi$
$11$	1.99769	0.602326	0.301163	+	0.953573i	$0.402625\pi$
$12$	14.1372	4.08106
$13$	−5.35442	−1.48505	−0.742524	−	0.669820i	$-0.766371\pi$
$13$	−5.35442	−1.48505	−0.742524	+	0.669820i	$0.766371\pi$
$14$	9.20942	2.46132
$15$	−8.79672	−2.27130
$16$	14.4528	3.61321
$17$	1.58589	0.384635	0.192318	−	0.981333i	$-0.438400\pi$
$17$	1.58589	0.384635	0.192318	+	0.981333i	$0.438400\pi$
$18$	−10.4187	−2.45571
$19$	5.90174	1.35395	0.676976	−	0.736005i	$-0.263290\pi$
$19$	5.90174	1.35395	0.676976	+	0.736005i	$0.263290\pi$
$20$	−18.2154	−4.07308
$21$	−8.83957	−1.92895
$22$	−5.43817	−1.15942
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−24.2589	−4.95183
$25$	6.33429	1.26686
$26$	14.5760	2.85858
$27$	2.16156	0.415992
$28$	−18.3041	−3.45915
$29$	2.91547	0.541389	0.270694	−	0.962665i	$-0.412747\pi$
$29$	2.91547	0.541389	0.270694	+	0.962665i	$0.412747\pi$
$30$	23.9467	4.37205
$31$	−6.92307	−1.24342	−0.621710	−	0.783248i	$-0.713562\pi$
$31$	−6.92307	−1.24342	−0.621710	+	0.783248i	$0.713562\pi$
$32$	−20.7754	−3.67261
$33$	5.21977	0.908646
$34$	−4.31716	−0.740387
$35$	11.3895	1.92518
$36$	20.7076	3.45126
$37$	1.21509	0.199760	0.0998801	−	0.994999i	$-0.468154\pi$
$37$	1.21509	0.199760	0.0998801	+	0.994999i	$0.468154\pi$
$38$	−16.0659	−2.60623
$39$	−13.9906	−2.24028
$40$	31.2568	4.94214
$41$	8.92006	1.39308	0.696539	−	0.717518i	$-0.254722\pi$
$41$	8.92006	1.39308	0.696539	+	0.717518i	$0.254722\pi$
$42$	24.0633	3.71305
$43$	3.74678	0.571378	0.285689	−	0.958322i	$-0.407778\pi$
$43$	3.74678	0.571378	0.285689	+	0.958322i	$0.407778\pi$
$44$	10.8086	1.62945
$45$	−12.8850	−1.92079
$46$	−2.72223	−0.401371
$47$	−6.58370	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$47$	−6.58370	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$48$	37.7639	5.45075
$49$	4.44498	0.634998
$50$	−17.2434	−2.43859
$51$	4.14378	0.580246
$52$	−28.9703	−4.01745
$53$	6.93088	0.952029	0.476015	−	0.879437i	$-0.342081\pi$
$53$	6.93088	0.952029	0.476015	+	0.879437i	$0.342081\pi$
$54$	−5.88426	−0.800747
$55$	−6.72551	−0.906868
$56$	31.4091	4.19722
$57$	15.4207	2.04252
$58$	−7.93658	−1.04212
$59$	10.3769	1.35095	0.675477	−	0.737381i	$-0.263938\pi$
$59$	10.3769	1.35095	0.675477	+	0.737381i	$0.263938\pi$
$60$	−47.5950	−6.14448
$61$	−6.67661	−0.854853	−0.427426	−	0.904050i	$-0.640580\pi$
$61$	−6.67661	−0.854853	−0.427426	+	0.904050i	$0.640580\pi$
$62$	18.8462	2.39347
$63$	−12.9478	−1.63127
$64$	27.6498	3.45623
$65$	18.0264	2.23590
$66$	−14.2094	−1.74906
$67$	−13.5866	−1.65987	−0.829934	−	0.557862i	$-0.811622\pi$
$67$	−13.5866	−1.65987	−0.829934	+	0.557862i	$0.811622\pi$
$68$	8.58053	1.04054
$69$	2.61290	0.314557
$70$	−31.0049	−3.70579
$71$	1.16563	0.138335	0.0691673	−	0.997605i	$-0.477966\pi$
$71$	1.16563	0.138335	0.0691673	+	0.997605i	$0.477966\pi$
$72$	−35.5333	−4.18764
$73$	6.20236	0.725931	0.362966	−	0.931803i	$-0.381764\pi$
$73$	6.20236	0.725931	0.362966	+	0.931803i	$0.381764\pi$
$74$	−3.30776	−0.384520
$75$	16.5509	1.91113
$76$	31.9316	3.66280
$77$	−6.75827	−0.770177
$78$	38.0856	4.31234
$79$	−6.89733	−0.776010	−0.388005	−	0.921657i	$-0.626836\pi$
$79$	−6.89733	−0.776010	−0.388005	+	0.921657i	$0.626836\pi$
$80$	−48.6576	−5.44008
$81$	−5.83385	−0.648205
$82$	−24.2825	−2.68155
$83$	−5.22799	−0.573847	−0.286923	−	0.957954i	$-0.592632\pi$
$83$	−5.22799	−0.573847	−0.286923	+	0.957954i	$0.592632\pi$
$84$	−47.8268	−5.21833
$85$	−5.33913	−0.579110
$86$	−10.1996	−1.09985
$87$	7.61784	0.816718
$88$	−18.5471	−1.97713
$89$	−9.89423	−1.04879	−0.524393	−	0.851476i	$-0.675708\pi$
$89$	−9.89423	−1.04879	−0.524393	+	0.851476i	$0.675708\pi$
$90$	35.0760	3.69734
$91$	18.1142	1.89889
$92$	5.41054	0.564088
$93$	−18.0893	−1.87577
$94$	17.9224	1.84855
$95$	−19.8691	−2.03852
$96$	−54.2842	−5.54036
$97$	3.59806	0.365328	0.182664	−	0.983175i	$-0.441528\pi$
$97$	3.59806	0.365328	0.182664	+	0.983175i	$0.441528\pi$
$98$	−12.1003	−1.22231
$99$	7.64569	0.768420
$100$	34.2719	3.42719
$101$	−3.44824	−0.343113	−0.171556	−	0.985174i	$-0.554880\pi$
$101$	−3.44824	−0.343113	−0.171556	+	0.985174i	$0.554880\pi$
$102$	−11.2803	−1.11692
$103$	6.34629	0.625319	0.312660	−	0.949865i	$-0.398780\pi$
$103$	6.34629	0.625319	0.312660	+	0.949865i	$0.398780\pi$
$104$	49.7118	4.87465
$105$	29.7597	2.90425
$106$	−18.8674	−1.83257
$107$	9.16000	0.885530	0.442765	−	0.896638i	$-0.353998\pi$
$107$	9.16000	0.885530	0.442765	+	0.896638i	$0.353998\pi$
$108$	11.6952	1.12537
$109$	10.2281	0.979671	0.489836	−	0.871815i	$-0.337057\pi$
$109$	10.2281	0.979671	0.489836	+	0.871815i	$0.337057\pi$
$110$	18.3084	1.74564
$111$	3.17492	0.301350
$112$	−48.8946	−4.62010
$113$	−5.11817	−0.481477	−0.240738	−	0.970590i	$-0.577390\pi$
$113$	−5.11817	−0.481477	−0.240738	+	0.970590i	$0.577390\pi$
$114$	−41.9786	−3.93166
$115$	−3.36664	−0.313941
$116$	15.7743	1.46460
$117$	−20.4928	−1.89456
$118$	−28.2482	−2.60046
$119$	−5.36514	−0.491822
$120$	81.6711	7.45551
$121$	−7.00923	−0.637203
$122$	18.1753	1.64551
$123$	23.3072	2.10154
$124$	−37.4575	−3.36378
$125$	−4.49209	−0.401785
$126$	35.2469	3.14004
$127$	6.24984	0.554583	0.277292	−	0.960786i	$-0.410563\pi$
$127$	6.24984	0.554583	0.277292	+	0.960786i	$0.410563\pi$
$128$	−33.7183	−2.98030
$129$	9.78997	0.861959
$130$	−49.0721	−4.30390
$131$	10.1151	0.883761	0.441880	−	0.897074i	$-0.354312\pi$
$131$	10.1151	0.883761	0.441880	+	0.897074i	$0.354312\pi$
$132$	28.2418	2.45813
$133$	−19.9658	−1.73126
$134$	36.9859	3.19509
$135$	−7.27720	−0.626322
$136$	−14.7238	−1.26256
$137$	−4.12044	−0.352033	−0.176016	−	0.984387i	$-0.556321\pi$
$137$	−4.12044	−0.352033	−0.176016	+	0.984387i	$0.556321\pi$
$138$	−7.11292	−0.605492
$139$	12.0297	1.02035	0.510174	−	0.860071i	$-0.329581\pi$
$139$	12.0297	1.02035	0.510174	+	0.860071i	$0.329581\pi$
$140$	61.6233	5.20812
$141$	−17.2026	−1.44872
$142$	−3.17311	−0.266281
$143$	−10.6965	−0.894483
$144$	55.3148	4.60957
$145$	−9.81534	−0.815120
$146$	−16.8842	−1.39735
$147$	11.6143	0.957932
$148$	6.57431	0.540405
$149$	−8.92886	−0.731480	−0.365740	−	0.930717i	$-0.619184\pi$
$149$	−8.92886	−0.731480	−0.365740	+	0.930717i	$0.619184\pi$
$150$	−45.0554	−3.67875
$151$	12.0712	0.982344	0.491172	−	0.871063i	$-0.336569\pi$
$151$	12.0712	0.982344	0.491172	+	0.871063i	$0.336569\pi$
$152$	−54.7933	−4.44433
$153$	6.06963	0.490700
$154$	18.3976	1.48252
$155$	23.3075	1.87210
$156$	−75.6965	−6.06057
$157$	−4.64737	−0.370901	−0.185450	−	0.982654i	$-0.559374\pi$
$157$	−4.64737	−0.370901	−0.185450	+	0.982654i	$0.559374\pi$
$158$	18.7761	1.49375
$159$	18.1097	1.43619
$160$	69.9435	5.52952
$161$	−3.38304	−0.266621
$162$	15.8811	1.24773
$163$	−7.59927	−0.595221	−0.297611	−	0.954687i	$-0.596190\pi$
$163$	−7.59927	−0.595221	−0.297611	+	0.954687i	$0.596190\pi$
$164$	48.2623	3.76865
$165$	−17.5731	−1.36807
$166$	14.2318	1.10460
$167$	5.21436	0.403499	0.201750	−	0.979437i	$-0.435337\pi$
$167$	5.21436	0.403499	0.201750	+	0.979437i	$0.435337\pi$
$168$	82.0689	6.33175
$169$	15.6698	1.20537
$170$	14.5344	1.11473
$171$	22.5875	1.72731
$172$	20.2721	1.54573
$173$	21.8786	1.66340	0.831700	−	0.555225i	$-0.187368\pi$
$173$	21.8786	1.66340	0.831700	+	0.555225i	$0.187368\pi$
$174$	−20.7375	−1.57211
$175$	−21.4292	−1.61989
$176$	28.8723	2.17633
$177$	27.1138	2.03799
$178$	26.9344	2.01882
$179$	1.77668	0.132795	0.0663975	−	0.997793i	$-0.478849\pi$
$179$	1.77668	0.132795	0.0663975	+	0.997793i	$0.478849\pi$
$180$	−69.7150	−5.19625
$181$	16.6331	1.23633	0.618166	−	0.786048i	$-0.287876\pi$
$181$	16.6331	1.23633	0.618166	+	0.786048i	$0.287876\pi$
$182$	−49.3111	−3.65518
$183$	−17.4453	−1.28960
$184$	−9.28427	−0.684445
$185$	−4.09079	−0.300761
$186$	49.2433	3.61069
$187$	3.16812	0.231676
$188$	−35.6214	−2.59796
$189$	−7.31265	−0.531917
$190$	54.0882	3.92397
$191$	8.89123	0.643347	0.321673	−	0.946851i	$-0.395755\pi$
$191$	8.89123	0.643347	0.321673	+	0.946851i	$0.395755\pi$
$192$	72.2463	5.21393
$193$	−18.3345	−1.31975	−0.659873	−	0.751377i	$-0.729390\pi$
$193$	−18.3345	−1.31975	−0.659873	+	0.751377i	$0.729390\pi$
$194$	−9.79475	−0.703222
$195$	47.1013	3.37299
$196$	24.0498	1.71784
$197$	7.20568	0.513383	0.256692	−	0.966493i	$-0.417368\pi$
$197$	7.20568	0.513383	0.256692	+	0.966493i	$0.417368\pi$
$198$	−20.8133	−1.47914
$199$	27.0058	1.91439	0.957195	−	0.289442i	$-0.0934699\pi$
$199$	27.0058	1.91439	0.957195	+	0.289442i	$0.0934699\pi$
$200$	−58.8093	−4.15844
$201$	−35.5005	−2.50401
$202$	9.38691	0.660460
$203$	−9.86316	−0.692258
$204$	22.4201	1.56972
$205$	−30.0307	−2.09743
$206$	−17.2761	−1.20368
$207$	3.82726	0.266013
$208$	−77.3865	−5.36579
$209$	11.7899	0.815521
$210$	−81.0127	−5.59041
$211$	−24.7612	−1.70463	−0.852316	−	0.523027i	$-0.824803\pi$
$211$	−24.7612	−1.70463	−0.852316	+	0.523027i	$0.824803\pi$
$212$	37.4998	2.57550
$213$	3.04567	0.208686
$214$	−24.9356	−1.70456
$215$	−12.6141	−0.860272
$216$	−20.0685	−1.36549
$217$	23.4210	1.58992
$218$	−27.8432	−1.88578
$219$	16.2062	1.09511
$220$	−36.3886	−2.45332
$221$	−8.49152	−0.571202
$222$	−8.64287	−0.580071
$223$	−26.7889	−1.79392	−0.896959	−	0.442114i	$-0.854229\pi$
$223$	−26.7889	−1.79392	−0.896959	+	0.442114i	$0.854229\pi$
$224$	70.2842	4.69606
$225$	24.2430	1.61620
$226$	13.9328	0.926798
$227$	17.9741	1.19298	0.596492	−	0.802619i	$-0.296561\pi$
$227$	17.9741	1.19298	0.596492	+	0.802619i	$0.296561\pi$
$228$	83.4342	5.52556
$229$	−24.7008	−1.63228	−0.816139	−	0.577856i	$-0.803889\pi$
$229$	−24.7008	−1.63228	−0.816139	+	0.577856i	$0.803889\pi$
$230$	9.16478	0.604308
$231$	−17.6587	−1.16186
$232$	−27.0680	−1.77710
$233$	−16.5551	−1.08456	−0.542279	−	0.840199i	$-0.682438\pi$
$233$	−16.5551	−1.08456	−0.542279	+	0.840199i	$0.682438\pi$
$234$	55.7860	3.64685
$235$	22.1650	1.44588
$236$	56.1444	3.65469
$237$	−18.0220	−1.17066
$238$	14.6051	0.946711
$239$	0.270694	0.0175097	0.00875486	−	0.999962i	$-0.497213\pi$
$239$	0.270694	0.0175097	0.00875486	+	0.999962i	$0.497213\pi$
$240$	−127.138	−8.20669
$241$	−28.1727	−1.81477	−0.907383	−	0.420305i	$-0.861923\pi$
$241$	−28.1727	−1.81477	−0.907383	+	0.420305i	$0.861923\pi$
$242$	19.0807	1.22656
$243$	−21.7280	−1.39385
$244$	−36.1241	−2.31261
$245$	−14.9647	−0.956058
$246$	−63.4477	−4.04528
$247$	−31.6004	−2.01068
$248$	64.2756	4.08151
$249$	−13.6602	−0.865682
$250$	12.2285	0.773399
$251$	−12.4449	−0.785513	−0.392757	−	0.919642i	$-0.628479\pi$
$251$	−12.4449	−0.785513	−0.392757	+	0.919642i	$0.628479\pi$
$252$	−70.0546	−4.41302
$253$	1.99769	0.125594
$254$	−17.0135	−1.06752
$255$	−13.9506	−0.873623
$256$	36.4893	2.28058
$257$	11.4069	0.711542	0.355771	−	0.934573i	$-0.384218\pi$
$257$	11.4069	0.711542	0.355771	+	0.934573i	$0.384218\pi$
$258$	−26.6505	−1.65919
$259$	−4.11071	−0.255427
$260$	97.5326	6.04871
$261$	11.1583	0.690679
$262$	−27.5356	−1.70116
$263$	11.1948	0.690300	0.345150	−	0.938548i	$-0.387828\pi$
$263$	11.1948	0.690300	0.345150	+	0.938548i	$0.387828\pi$
$264$	−48.4618	−2.98262
$265$	−23.3338	−1.43338
$266$	54.3516	3.33251
$267$	−25.8527	−1.58216
$268$	−73.5108	−4.49039
$269$	18.4485	1.12482	0.562412	−	0.826857i	$-0.309874\pi$
$269$	18.4485	1.12482	0.562412	+	0.826857i	$0.309874\pi$
$270$	19.8102	1.20561
$271$	−28.0703	−1.70515	−0.852573	−	0.522607i	$-0.824959\pi$
$271$	−28.0703	−1.70515	−0.852573	+	0.522607i	$0.824959\pi$
$272$	22.9206	1.38977
$273$	47.3307	2.86459
$274$	11.2168	0.677630
$275$	12.6540	0.763062
$276$	14.1372	0.850960
$277$	−19.4423	−1.16817	−0.584086	−	0.811692i	$-0.698547\pi$
$277$	−19.4423	−1.16817	−0.584086	+	0.811692i	$0.698547\pi$
$278$	−32.7477	−1.96407
$279$	−26.4964	−1.58630
$280$	−105.743	−6.31937
$281$	−11.3898	−0.679458	−0.339729	−	0.940523i	$-0.610335\pi$
$281$	−11.3898	−0.679458	−0.339729	+	0.940523i	$0.610335\pi$
$282$	46.8294	2.78865
$283$	−20.7927	−1.23600	−0.618000	−	0.786178i	$-0.712057\pi$
$283$	−20.7927	−1.23600	−0.618000	+	0.786178i	$0.712057\pi$
$284$	6.30668	0.374232
$285$	−51.9159	−3.07523
$286$	29.1182	1.72180
$287$	−30.1769	−1.78129
$288$	−79.5130	−4.68535
$289$	−14.4849	−0.852056
$290$	26.7196	1.56903
$291$	9.40138	0.551119
$292$	33.5581	1.96384
$293$	16.8898	0.986713	0.493357	−	0.869827i	$-0.335770\pi$
$293$	16.8898	0.986713	0.493357	+	0.869827i	$0.335770\pi$
$294$	−31.6168	−1.84393
$295$	−34.9352	−2.03401
$296$	−11.2813	−0.655710
$297$	4.31813	0.250563
$298$	24.3064	1.40803
$299$	−5.35442	−0.309654
$300$	89.5492	5.17013
$301$	−12.6755	−0.730604
$302$	−32.8607	−1.89092
$303$	−9.00992	−0.517606
$304$	85.2969	4.89211
$305$	22.4778	1.28707
$306$	−16.5229	−0.944552
$307$	19.8060	1.13039	0.565193	−	0.824959i	$-0.308802\pi$
$307$	19.8060	1.13039	0.565193	+	0.824959i	$0.308802\pi$
$308$	−36.5659	−2.08354
$309$	16.5823	0.943332
$310$	−63.4484	−3.60363
$311$	−4.82450	−0.273572	−0.136786	−	0.990601i	$-0.543677\pi$
$311$	−4.82450	−0.273572	−0.136786	+	0.990601i	$0.543677\pi$
$312$	129.892	7.35370
$313$	−6.35011	−0.358929	−0.179465	−	0.983764i	$-0.557437\pi$
$313$	−6.35011	−0.358929	−0.179465	+	0.983764i	$0.557437\pi$
$314$	12.6512	0.713949
$315$	43.5906	2.45605
$316$	−37.3182	−2.09931
$317$	−16.5517	−0.929639	−0.464819	−	0.885406i	$-0.653881\pi$
$317$	−16.5517	−0.929639	−0.464819	+	0.885406i	$0.653881\pi$
$318$	−49.2988	−2.76454
$319$	5.82420	0.326093
$320$	−93.0871	−5.20373
$321$	23.9342	1.33588
$322$	9.20942	0.513221
$323$	9.35952	0.520778
$324$	−31.5642	−1.75357
$325$	−33.9164	−1.88135
$326$	20.6870	1.14575
$327$	26.7250	1.47789
$328$	−82.8162	−4.57276
$329$	22.2730	1.22795
$330$	47.8381	2.63340
$331$	−33.0004	−1.81387	−0.906934	−	0.421273i	$-0.861583\pi$
$331$	−33.0004	−1.81387	−0.906934	+	0.421273i	$0.861583\pi$
$332$	−28.2862	−1.55241
$333$	4.65048	0.254845
$334$	−14.1947	−0.776698
$335$	45.7413	2.49911
$336$	−127.757	−6.96971
$337$	−27.2167	−1.48259	−0.741294	−	0.671180i	$-0.765788\pi$
$337$	−27.2167	−1.48259	−0.741294	+	0.671180i	$0.765788\pi$
$338$	−42.6567	−2.32022
$339$	−13.3733	−0.726337
$340$	−28.8876	−1.56665
$341$	−13.8301	−0.748944
$342$	−61.4884	−3.32491
$343$	8.64373	0.466718
$344$	−34.7861	−1.87554
$345$	−8.79672	−0.473599
$346$	−59.5586	−3.20189
$347$	−10.5250	−0.565014	−0.282507	−	0.959265i	$-0.591166\pi$
$347$	−10.5250	−0.565014	−0.282507	+	0.959265i	$0.591166\pi$
$348$	41.2166	2.20944
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	58.3352	3.11815
$351$	−11.5739	−0.617768
$352$	−41.5029	−2.21211
$353$	−32.4586	−1.72760	−0.863798	−	0.503838i	$-0.831921\pi$
$353$	−32.4586	−1.72760	−0.863798	+	0.503838i	$0.831921\pi$
$354$	−73.8099	−3.92295
$355$	−3.92426	−0.208278
$356$	−53.5331	−2.83725
$357$	−14.0186	−0.741943
$358$	−4.83652	−0.255618
$359$	22.2564	1.17465	0.587324	−	0.809352i	$-0.300182\pi$
$359$	22.2564	1.17465	0.587324	+	0.809352i	$0.300182\pi$
$360$	119.628	6.30496
$361$	15.8305	0.833187
$362$	−45.2792	−2.37982
$363$	−18.3144	−0.961259
$364$	98.0077	5.13700
$365$	−20.8811	−1.09297
$366$	47.4902	2.48235
$367$	−24.2304	−1.26481	−0.632407	−	0.774636i	$-0.717933\pi$
$367$	−24.2304	−1.26481	−0.632407	+	0.774636i	$0.717933\pi$
$368$	14.4528	0.753406
$369$	34.1394	1.77723
$370$	11.1361	0.578936
$371$	−23.4475	−1.21733
$372$	−97.8729	−5.07447
$373$	2.12664	0.110113	0.0550567	−	0.998483i	$-0.482466\pi$
$373$	2.12664	0.110113	0.0550567	+	0.998483i	$0.482466\pi$
$374$	−8.62435	−0.445955
$375$	−11.7374	−0.606117
$376$	61.1249	3.15227
$377$	−15.6106	−0.803988
$378$	19.9067	1.02389
$379$	7.91943	0.406794	0.203397	−	0.979096i	$-0.434802\pi$
$379$	7.91943	0.406794	0.203397	+	0.979096i	$0.434802\pi$
$380$	−107.502	−5.51475
$381$	16.3302	0.836622
$382$	−24.2040	−1.23838
$383$	−31.4801	−1.60856	−0.804280	−	0.594251i	$-0.797449\pi$
$383$	−31.4801	−1.60856	−0.804280	+	0.594251i	$0.797449\pi$
$384$	−88.1026	−4.49597
$385$	22.7527	1.15959
$386$	49.9108	2.54039
$387$	14.3399	0.728938
$388$	19.4674	0.988309
$389$	−2.44643	−0.124039	−0.0620196	−	0.998075i	$-0.519754\pi$
$389$	−2.44643	−0.124039	−0.0620196	+	0.998075i	$0.519754\pi$
$390$	−128.221	−6.49270
$391$	1.58589	0.0802020
$392$	−41.2684	−2.08437
$393$	26.4298	1.33321
$394$	−19.6155	−0.988215
$395$	23.2208	1.16837
$396$	41.3673	2.07878
$397$	−16.4358	−0.824889	−0.412445	−	0.910983i	$-0.635325\pi$
$397$	−16.4358	−0.824889	−0.412445	+	0.910983i	$0.635325\pi$
$398$	−73.5160	−3.68503
$399$	−52.1688	−2.61171
$400$	91.5485	4.57743
$401$	−11.5723	−0.577894	−0.288947	−	0.957345i	$-0.593305\pi$
$401$	−11.5723	−0.577894	−0.288947	+	0.957345i	$0.593305\pi$
$402$	96.6405	4.81999
$403$	37.0690	1.84654
$404$	−18.6568	−0.928212
$405$	19.6405	0.975943
$406$	26.8498	1.33253
$407$	2.42738	0.120321
$408$	−38.4720	−1.90465
$409$	4.03643	0.199589	0.0997944	−	0.995008i	$-0.468181\pi$
$409$	4.03643	0.199589	0.0997944	+	0.995008i	$0.468181\pi$
$410$	81.7504	4.03736
$411$	−10.7663	−0.531062
$412$	34.3369	1.69166
$413$	−35.1054	−1.72742
$414$	−10.4187	−0.512051
$415$	17.6008	0.863989
$416$	111.240	5.45400
$417$	31.4325	1.53926
$418$	−32.0947	−1.56980
$419$	24.2706	1.18570	0.592849	−	0.805313i	$-0.298003\pi$
$419$	24.2706	1.18570	0.592849	+	0.805313i	$0.298003\pi$
$420$	161.016	7.85677
$421$	8.81421	0.429578	0.214789	−	0.976660i	$-0.431094\pi$
$421$	8.81421	0.429578	0.214789	+	0.976660i	$0.431094\pi$
$422$	67.4057	3.28126
$423$	−25.1976	−1.22515
$424$	−64.3481	−3.12502
$425$	10.0455	0.487279
$426$	−8.29102	−0.401701
$427$	22.5873	1.09307
$428$	49.5605	2.39560
$429$	−27.9488	−1.34938
$430$	34.3384	1.65594
$431$	−7.58988	−0.365592	−0.182796	−	0.983151i	$-0.558515\pi$
$431$	−7.58988	−0.365592	−0.182796	+	0.983151i	$0.558515\pi$
$432$	31.2407	1.50307
$433$	5.63124	0.270620	0.135310	−	0.990803i	$-0.456797\pi$
$433$	5.63124	0.270620	0.135310	+	0.990803i	$0.456797\pi$
$434$	−63.7575	−3.06046
$435$	−25.6465	−1.22966
$436$	55.3394	2.65027
$437$	5.90174	0.282319
$438$	−44.1169	−2.10799
$439$	−25.6170	−1.22263	−0.611317	−	0.791386i	$-0.709360\pi$
$439$	−25.6170	−1.22263	−0.611317	+	0.791386i	$0.709360\pi$
$440$	62.4415	2.97678
$441$	17.0121	0.810101
$442$	23.1159	1.09951
$443$	−41.0808	−1.95181	−0.975904	−	0.218199i	$-0.929982\pi$
$443$	−41.0808	−1.95181	−0.975904	+	0.218199i	$0.929982\pi$
$444$	17.1780	0.815233
$445$	33.3103	1.57906
$446$	72.9256	3.45313
$447$	−23.3302	−1.10348
$448$	−93.5405	−4.41937
$449$	30.8163	1.45431	0.727156	−	0.686472i	$-0.240842\pi$
$449$	30.8163	1.45431	0.727156	+	0.686472i	$0.240842\pi$
$450$	−65.9951	−3.11104
$451$	17.8195	0.839088
$452$	−27.6920	−1.30252
$453$	31.5410	1.48192
$454$	−48.9297	−2.29638
$455$	−60.9841	−2.85898
$456$	−143.170	−6.70454
$457$	8.16907	0.382133	0.191066	−	0.981577i	$-0.438805\pi$
$457$	8.16907	0.382133	0.191066	+	0.981577i	$0.438805\pi$
$458$	67.2414	3.14198
$459$	3.42800	0.160005
$460$	−18.2154	−0.849295
$461$	−40.1531	−1.87011	−0.935057	−	0.354497i	$-0.884652\pi$
$461$	−40.1531	−1.87011	−0.935057	+	0.354497i	$0.884652\pi$
$462$	48.0711	2.23647
$463$	−26.1350	−1.21460	−0.607298	−	0.794474i	$-0.707747\pi$
$463$	−26.1350	−1.21460	−0.607298	+	0.794474i	$0.707747\pi$
$464$	42.1368	1.95615
$465$	60.9003	2.82418
$466$	45.0667	2.08767
$467$	−33.2532	−1.53878	−0.769388	−	0.638782i	$-0.779439\pi$
$467$	−33.2532	−1.53878	−0.769388	+	0.638782i	$0.779439\pi$
$468$	−110.877	−5.12528
$469$	45.9641	2.12242
$470$	−60.3382	−2.78319
$471$	−12.1431	−0.559526
$472$	−96.3416	−4.43448
$473$	7.48490	0.344156
$474$	49.0602	2.25341
$475$	37.3834	1.71527
$476$	−29.0283	−1.33051
$477$	26.5263	1.21456
$478$	−0.736891	−0.0337046
$479$	2.02901	0.0927076	0.0463538	−	0.998925i	$-0.485240\pi$
$479$	2.02901	0.0927076	0.0463538	+	0.998925i	$0.485240\pi$
$480$	182.756	8.34161
$481$	−6.50612	−0.296653
$482$	76.6927	3.49326
$483$	−8.83957	−0.402214
$484$	−37.9237	−1.72381
$485$	−12.1134	−0.550040
$486$	59.1485	2.68303
$487$	6.92460	0.313784	0.156892	−	0.987616i	$-0.449853\pi$
$487$	6.92460	0.313784	0.156892	+	0.987616i	$0.449853\pi$
$488$	61.9875	2.80604
$489$	−19.8562	−0.897927
$490$	40.7373	1.84032
$491$	−13.4550	−0.607217	−0.303608	−	0.952797i	$-0.598191\pi$
$491$	−13.4550	−0.607217	−0.303608	+	0.952797i	$0.598191\pi$
$492$	126.105	5.68524
$493$	4.62362	0.208237
$494$	86.0235	3.87038
$495$	−25.7403	−1.15694
$496$	−100.058	−4.49274
$497$	−3.94337	−0.176884
$498$	37.1863	1.66636
$499$	−0.694030	−0.0310691	−0.0155345	−	0.999879i	$-0.504945\pi$
$499$	−0.694030	−0.0310691	−0.0155345	+	0.999879i	$0.504945\pi$
$500$	−24.3046	−1.08694
$501$	13.6246	0.608703
$502$	33.8778	1.51204
$503$	−31.6955	−1.41323	−0.706617	−	0.707596i	$-0.749780\pi$
$503$	−31.6955	−1.41323	−0.706617	+	0.707596i	$0.749780\pi$
$504$	120.211	5.35462
$505$	11.6090	0.516594
$506$	−5.43817	−0.241756
$507$	40.9436	1.81837
$508$	33.8150	1.50030
$509$	−26.2923	−1.16538	−0.582692	−	0.812693i	$-0.698001\pi$
$509$	−26.2923	−1.16538	−0.582692	+	0.812693i	$0.698001\pi$
$510$	37.9769	1.68164
$511$	−20.9828	−0.928227
$512$	−31.8958	−1.40961
$513$	12.7570	0.563234
$514$	−31.0522	−1.36965
$515$	−21.3657	−0.941486
$516$	52.9690	2.33183
$517$	−13.1522	−0.578433
$518$	11.1903	0.491674
$519$	57.1667	2.50934
$520$	−167.362	−7.33931
$521$	32.8721	1.44015	0.720077	−	0.693894i	$-0.244107\pi$
$521$	32.8721	1.44015	0.720077	+	0.693894i	$0.244107\pi$
$522$	−30.3754	−1.32949
$523$	−26.3977	−1.15429	−0.577145	−	0.816642i	$-0.695833\pi$
$523$	−26.3977	−1.15429	−0.577145	+	0.816642i	$0.695833\pi$
$524$	54.7281	2.39081
$525$	−55.9924	−2.44371
$526$	−30.4748	−1.32876
$527$	−10.9792	−0.478263
$528$	75.4405	3.28313
$529$	1.00000	0.0434783
$530$	63.5200	2.75913
$531$	39.7150	1.72348
$532$	−108.026	−4.68352
$533$	−47.7617	−2.06879
$534$	70.3769	3.04551
$535$	−30.8385	−1.33326
$536$	126.142	5.44849
$537$	4.64228	0.200329
$538$	−50.2210	−2.16518
$539$	8.87970	0.382476
$540$	−39.3736	−1.69437
$541$	21.3954	0.919862	0.459931	−	0.887955i	$-0.347874\pi$
$541$	21.3954	0.919862	0.459931	+	0.887955i	$0.347874\pi$
$542$	76.4137	3.28225
$543$	43.4608	1.86508
$544$	−32.9476	−1.41262
$545$	−34.4343	−1.47500
$546$	−128.845	−5.51406
$547$	35.0436	1.49836	0.749179	−	0.662368i	$-0.230448\pi$
$547$	35.0436	1.49836	0.749179	+	0.662368i	$0.230448\pi$
$548$	−22.2938	−0.952343
$549$	−25.5532	−1.09058
$550$	−34.4470	−1.46882
$551$	17.2063	0.733015
$552$	−24.2589	−1.03253
$553$	23.3340	0.992261
$554$	52.9263	2.24862
$555$	−10.6888	−0.453716
$556$	65.0873	2.76031
$557$	−29.9419	−1.26868	−0.634340	−	0.773054i	$-0.718728\pi$
$557$	−29.9419	−1.26868	−0.634340	+	0.773054i	$0.718728\pi$
$558$	72.1293	3.05348
$559$	−20.0618	−0.848524
$560$	164.611	6.95607
$561$	8.27799	0.349497
$562$	31.0056	1.30789
$563$	−2.94891	−0.124282	−0.0621408	−	0.998067i	$-0.519793\pi$
$563$	−2.94891	−0.124282	−0.0621408	+	0.998067i	$0.519793\pi$
$564$	−93.0752	−3.91917
$565$	17.2310	0.724916
$566$	56.6026	2.37919
$567$	19.7362	0.828841
$568$	−10.8220	−0.454081
$569$	−16.8531	−0.706520	−0.353260	−	0.935525i	$-0.614927\pi$
$569$	−16.8531	−0.706520	−0.353260	+	0.935525i	$0.614927\pi$
$570$	141.327	5.91954
$571$	21.5415	0.901483	0.450742	−	0.892655i	$-0.351160\pi$
$571$	21.5415	0.901483	0.450742	+	0.892655i	$0.351160\pi$
$572$	−57.8736	−2.41982
$573$	23.2319	0.970527
$574$	82.1486	3.42882
$575$	6.33429	0.264158
$576$	105.823	4.40930
$577$	−5.28750	−0.220122	−0.110061	−	0.993925i	$-0.535105\pi$
$577$	−5.28750	−0.220122	−0.110061	+	0.993925i	$0.535105\pi$
$578$	39.4314	1.64013
$579$	−47.9063	−1.99092
$580$	−53.1063	−2.20512
$581$	17.6865	0.733761
$582$	−25.5927	−1.06085
$583$	13.8457	0.573432
$584$	−57.5844	−2.38286
$585$	68.9918	2.85246
$586$	−45.9779	−1.89933
$587$	−9.99359	−0.412480	−0.206240	−	0.978501i	$-0.566123\pi$
$587$	−9.99359	−0.412480	−0.206240	+	0.978501i	$0.566123\pi$
$588$	62.8397	2.59146
$589$	−40.8581	−1.68353
$590$	95.1017	3.91528
$591$	18.8277	0.774469
$592$	17.5616	0.721775
$593$	−8.72777	−0.358407	−0.179203	−	0.983812i	$-0.557352\pi$
$593$	−8.72777	−0.358407	−0.179203	+	0.983812i	$0.557352\pi$
$594$	−11.7549	−0.482311
$595$	18.0625	0.740491
$596$	−48.3099	−1.97885
$597$	70.5636	2.88797
$598$	14.5760	0.596055
$599$	−34.3281	−1.40261	−0.701305	−	0.712862i	$-0.747399\pi$
$599$	−34.3281	−1.40261	−0.701305	+	0.712862i	$0.747399\pi$
$600$	−153.663	−6.27326
$601$	33.0678	1.34887	0.674433	−	0.738336i	$-0.264388\pi$
$601$	33.0678	1.34887	0.674433	+	0.738336i	$0.264388\pi$
$602$	34.5057	1.40635
$603$	−51.9995	−2.11758
$604$	65.3119	2.65750
$605$	23.5976	0.959379
$606$	24.5271	0.996345
$607$	−18.4655	−0.749490	−0.374745	−	0.927128i	$-0.622270\pi$
$607$	−18.4655	−0.749490	−0.374745	+	0.927128i	$0.622270\pi$
$608$	−122.611	−4.97254
$609$	−25.7715	−1.04431
$610$	−61.1897	−2.47750
$611$	35.2519	1.42614
$612$	32.8399	1.32748
$613$	−32.6184	−1.31744	−0.658722	−	0.752387i	$-0.728902\pi$
$613$	−32.6184	−1.31744	−0.658722	+	0.752387i	$0.728902\pi$
$614$	−53.9164	−2.17589
$615$	−78.4672	−3.16410
$616$	62.7456	2.52809
$617$	12.0872	0.486613	0.243306	−	0.969949i	$-0.421768\pi$
$617$	12.0872	0.486613	0.243306	+	0.969949i	$0.421768\pi$
$618$	−45.1407	−1.81583
$619$	−28.9709	−1.16444	−0.582220	−	0.813032i	$-0.697816\pi$
$619$	−28.9709	−1.16444	−0.582220	+	0.813032i	$0.697816\pi$
$620$	126.106	5.06454
$621$	2.16156	0.0867404
$622$	13.1334	0.526602
$623$	33.4726	1.34105
$624$	−202.204	−8.09462
$625$	−16.5482	−0.661928
$626$	17.2864	0.690905
$627$	30.8057	1.23026
$628$	−25.1448	−1.00339
$629$	1.92701	0.0768348
$630$	−118.664	−4.72768
$631$	4.15771	0.165516	0.0827580	−	0.996570i	$-0.473627\pi$
$631$	4.15771	0.165516	0.0827580	+	0.996570i	$0.473627\pi$
$632$	64.0366	2.54724
$633$	−64.6986	−2.57154
$634$	45.0577	1.78947
$635$	−21.0410	−0.834986
$636$	97.9833	3.88529
$637$	−23.8003	−0.943002
$638$	−15.8548	−0.627698
$639$	4.46117	0.176481
$640$	113.518	4.48717
$641$	13.3764	0.528336	0.264168	−	0.964477i	$-0.414903\pi$
$641$	13.3764	0.528336	0.264168	+	0.964477i	$0.414903\pi$
$642$	−65.1544	−2.57144
$643$	3.53081	0.139242	0.0696208	−	0.997574i	$-0.477821\pi$
$643$	3.53081	0.139242	0.0696208	+	0.997574i	$0.477821\pi$
$644$	−18.3041	−0.721282
$645$	−32.9593	−1.29777
$646$	−25.4788	−1.00245
$647$	−28.1761	−1.10772	−0.553858	−	0.832611i	$-0.686845\pi$
$647$	−28.1761	−1.10772	−0.553858	+	0.832611i	$0.686845\pi$
$648$	54.1630	2.12772
$649$	20.7298	0.813715
$650$	92.3284	3.62142
$651$	61.1969	2.39850
$652$	−41.1162	−1.61023
$653$	50.1117	1.96102	0.980511	−	0.196463i	$-0.0629455\pi$
$653$	50.1117	1.96102	0.980511	+	0.196463i	$0.0629455\pi$
$654$	−72.7515	−2.84481
$655$	−34.0540	−1.33060
$656$	128.920	5.03349
$657$	23.7381	0.926110
$658$	−60.6321	−2.36369
$659$	37.3654	1.45555	0.727775	−	0.685816i	$-0.240554\pi$
$659$	37.3654	1.45555	0.727775	+	0.685816i	$0.240554\pi$
$660$	−95.0800	−3.70098
$661$	39.1916	1.52437	0.762187	−	0.647357i	$-0.224126\pi$
$661$	39.1916	1.52437	0.762187	+	0.647357i	$0.224126\pi$
$662$	89.8348	3.49153
$663$	−22.1875	−0.861692
$664$	48.5381	1.88364
$665$	67.2179	2.60660
$666$	−12.6597	−0.490553
$667$	2.91547	0.112887
$668$	28.2125	1.09157
$669$	−69.9968	−2.70623
$670$	−124.518	−4.81056
$671$	−13.3378	−0.514900
$672$	183.646	7.08429
$673$	4.09460	0.157835	0.0789177	−	0.996881i	$-0.474854\pi$
$673$	4.09460	0.157835	0.0789177	+	0.996881i	$0.474854\pi$
$674$	74.0901	2.85385
$675$	13.6920	0.527003
$676$	84.7819	3.26084
$677$	21.6174	0.830824	0.415412	−	0.909633i	$-0.363637\pi$
$677$	21.6174	0.830824	0.415412	+	0.909633i	$0.363637\pi$
$678$	36.4051	1.39813
$679$	−12.1724	−0.467133
$680$	49.5700	1.90092
$681$	46.9646	1.79969
$682$	37.6488	1.44165
$683$	−17.0761	−0.653398	−0.326699	−	0.945128i	$-0.605936\pi$
$683$	−17.0761	−0.653398	−0.326699	+	0.945128i	$0.605936\pi$
$684$	122.211	4.67284
$685$	13.8720	0.530024
$686$	−23.5302	−0.898388
$687$	−64.5409	−2.46239
$688$	54.1516	2.06451
$689$	−37.1108	−1.41381
$690$	23.9467	0.911635
$691$	−14.5688	−0.554224	−0.277112	−	0.960838i	$-0.589377\pi$
$691$	−14.5688	−0.554224	−0.277112	+	0.960838i	$0.589377\pi$
$692$	118.375	4.49995
$693$	−25.8657	−0.982556
$694$	28.6516	1.08760
$695$	−40.4998	−1.53624
$696$	−70.7260	−2.68086
$697$	14.1462	0.535827
$698$	−2.72223	−0.103038
$699$	−43.2568	−1.63612
$700$	−115.943	−4.38225
$701$	−44.1287	−1.66672	−0.833360	−	0.552731i	$-0.813586\pi$
$701$	−44.1287	−1.66672	−0.833360	+	0.552731i	$0.813586\pi$
$702$	31.5068	1.18915
$703$	7.17117	0.270466
$704$	55.2358	2.08178
$705$	57.9150	2.18120
$706$	88.3598	3.32546
$707$	11.6656	0.438728
$708$	146.700	5.51332
$709$	−21.8124	−0.819181	−0.409591	−	0.912269i	$-0.634328\pi$
$709$	−21.8124	−0.819181	−0.409591	+	0.912269i	$0.634328\pi$
$710$	10.6827	0.400916
$711$	−26.3979	−0.989998
$712$	91.8607	3.44262
$713$	−6.92307	−0.259271
$714$	38.1618	1.42817
$715$	36.0112	1.34674
$716$	9.61278	0.359246
$717$	0.707296	0.0264145
$718$	−60.5870	−2.26109
$719$	−31.5344	−1.17603	−0.588017	−	0.808849i	$-0.700091\pi$
$719$	−31.5344	−1.17603	−0.588017	+	0.808849i	$0.700091\pi$
$720$	−186.225	−6.94021
$721$	−21.4698	−0.799577
$722$	−43.0944	−1.60381
$723$	−73.6127	−2.73768
$724$	89.9942	3.34461
$725$	18.4674	0.685863
$726$	49.8561	1.85034
$727$	18.7295	0.694639	0.347320	−	0.937747i	$-0.387092\pi$
$727$	18.7295	0.694639	0.347320	+	0.937747i	$0.387092\pi$
$728$	−168.177	−6.23307
$729$	−39.2715	−1.45450
$730$	56.8433	2.10386
$731$	5.94198	0.219772
$732$	−94.3887	−3.48871
$733$	44.1479	1.63064	0.815320	−	0.579010i	$-0.196561\pi$
$733$	44.1479	1.63064	0.815320	+	0.579010i	$0.196561\pi$
$734$	65.9606	2.43465
$735$	−39.1013	−1.44227
$736$	−20.7754	−0.765792
$737$	−27.1418	−0.999782
$738$	−92.9353	−3.42100
$739$	23.6669	0.870602	0.435301	−	0.900285i	$-0.356642\pi$
$739$	23.6669	0.870602	0.435301	+	0.900285i	$0.356642\pi$
$740$	−22.1334	−0.813638
$741$	−82.5687	−3.03324
$742$	63.8294	2.34325
$743$	28.1197	1.03161	0.515807	−	0.856705i	$-0.327492\pi$
$743$	28.1197	1.03161	0.515807	+	0.856705i	$0.327492\pi$
$744$	167.946	6.15720
$745$	30.0603	1.10132
$746$	−5.78922	−0.211958
$747$	−20.0089	−0.732087
$748$	17.1412	0.626746
$749$	−30.9887	−1.13230
$750$	31.9519	1.16672
$751$	12.1328	0.442732	0.221366	−	0.975191i	$-0.428948\pi$
$751$	12.1328	0.442732	0.221366	+	0.975191i	$0.428948\pi$
$752$	−95.1532	−3.46988
$753$	−32.5172	−1.18499
$754$	42.4957	1.54760
$755$	−40.6396	−1.47903
$756$	−39.5654	−1.43898
$757$	−47.2142	−1.71603	−0.858014	−	0.513627i	$-0.828302\pi$
$757$	−47.2142	−1.71603	−0.858014	+	0.513627i	$0.828302\pi$
$758$	−21.5585	−0.783040
$759$	5.21977	0.189466
$760$	184.470	6.69142
$761$	−32.7039	−1.18552	−0.592758	−	0.805381i	$-0.701961\pi$
$761$	−32.7039	−1.18552	−0.592758	+	0.805381i	$0.701961\pi$
$762$	−44.4546	−1.61042
$763$	−34.6020	−1.25268
$764$	48.1063	1.74043
$765$	−20.4343	−0.738803
$766$	85.6962	3.09633
$767$	−55.5621	−2.00623
$768$	95.3431	3.44040
$769$	−29.1321	−1.05053	−0.525266	−	0.850938i	$-0.676034\pi$
$769$	−29.1321	−1.05053	−0.525266	+	0.850938i	$0.676034\pi$
$770$	−61.9381	−2.23209
$771$	29.8051	1.07340
$772$	−99.1996	−3.57027
$773$	25.7033	0.924482	0.462241	−	0.886754i	$-0.347046\pi$
$773$	25.7033	0.924482	0.462241	+	0.886754i	$0.347046\pi$
$774$	−39.0365	−1.40314
$775$	−43.8527	−1.57524
$776$	−33.4053	−1.19918
$777$	−10.7409	−0.385328
$778$	6.65976	0.238764
$779$	52.6439	1.88616
$780$	254.843	9.12485
$781$	2.32856	0.0833226
$782$	−4.31716	−0.154381
$783$	6.30196	0.225214
$784$	64.2427	2.29438
$785$	15.6460	0.558431
$786$	−71.9480	−2.56630
$787$	−1.28777	−0.0459041	−0.0229521	−	0.999737i	$-0.507307\pi$
$787$	−1.28777	−0.0459041	−0.0229521	+	0.999737i	$0.507307\pi$
$788$	38.9866	1.38884
$789$	29.2509	1.04136
$790$	−63.2125	−2.24900
$791$	17.3150	0.615650
$792$	−70.9846	−2.52233
$793$	35.7494	1.26950
$794$	44.7420	1.58784
$795$	−60.9690	−2.16235
$796$	146.116	5.17894
$797$	12.8018	0.453463	0.226732	−	0.973957i	$-0.427196\pi$
$797$	12.8018	0.453463	0.226732	+	0.973957i	$0.427196\pi$
$798$	142.016	5.02730
$799$	−10.4410	−0.369377
$800$	−131.598	−4.65268
$801$	−37.8678	−1.33799
$802$	31.5025	1.11239
$803$	12.3904	0.437247
$804$	−192.077	−6.77402
$805$	11.3895	0.401427
$806$	−100.910	−3.55441
$807$	48.2041	1.69686
$808$	32.0144	1.12626
$809$	−42.8114	−1.50517	−0.752584	−	0.658496i	$-0.771193\pi$
$809$	−42.8114	−1.50517	−0.752584	+	0.658496i	$0.771193\pi$
$810$	−53.4659	−1.87860
$811$	29.9408	1.05136	0.525682	−	0.850681i	$-0.323810\pi$
$811$	29.9408	1.05136	0.525682	+	0.850681i	$0.323810\pi$
$812$	−53.3650	−1.87274
$813$	−73.3449	−2.57232
$814$	−6.60789	−0.231606
$815$	25.5841	0.896170
$816$	59.8894	2.09655
$817$	22.1125	0.773619
$818$	−10.9881	−0.384190
$819$	69.3279	2.42251
$820$	−162.482	−5.67412
$821$	23.0361	0.803967	0.401984	−	0.915647i	$-0.368321\pi$
$821$	23.0361	0.803967	0.401984	+	0.915647i	$0.368321\pi$
$822$	29.3084	1.02225
$823$	46.0445	1.60501	0.802505	−	0.596645i	$-0.203500\pi$
$823$	46.0445	1.60501	0.802505	+	0.596645i	$0.203500\pi$
$824$	−58.9207	−2.05260
$825$	33.0636	1.15113
$826$	95.5650	3.32513
$827$	−1.77430	−0.0616985	−0.0308492	−	0.999524i	$-0.509821\pi$
$827$	−1.77430	−0.0616985	−0.0308492	+	0.999524i	$0.509821\pi$
$828$	20.7076	0.719637
$829$	−53.1997	−1.84770	−0.923851	−	0.382752i	$-0.874976\pi$
$829$	−53.1997	−1.84770	−0.923851	+	0.382752i	$0.874976\pi$
$830$	−47.9134	−1.66310
$831$	−50.8007	−1.76226
$832$	−148.049	−5.13266
$833$	7.04926	0.244243
$834$	−85.5665	−2.96293
$835$	−17.5549	−0.607512
$836$	63.7894	2.20620
$837$	−14.9646	−0.517253
$838$	−66.0703	−2.28236
$839$	23.3637	0.806605	0.403302	−	0.915067i	$-0.367862\pi$
$839$	23.3637	0.806605	0.403302	+	0.915067i	$0.367862\pi$
$840$	−276.297	−9.53315
$841$	−20.5000	−0.706898
$842$	−23.9943	−0.826898
$843$	−29.7604	−1.02500
$844$	−133.971	−4.61149
$845$	−52.7546	−1.81481
$846$	68.5936	2.35830
$847$	23.7125	0.814773
$848$	100.171	3.43988
$849$	−54.3294	−1.86458
$850$	−27.3462	−0.937966
$851$	1.21509	0.0416529
$852$	16.4787	0.564552
$853$	31.1974	1.06818	0.534089	−	0.845428i	$-0.320655\pi$
$853$	31.1974	1.06818	0.534089	+	0.845428i	$0.320655\pi$
$854$	−61.4877	−2.10407
$855$	−76.0441	−2.60065
$856$	−85.0439	−2.90674
$857$	18.1807	0.621040	0.310520	−	0.950567i	$-0.399497\pi$
$857$	18.1807	0.621040	0.310520	+	0.950567i	$0.399497\pi$
$858$	76.0831	2.59744
$859$	−15.4672	−0.527736	−0.263868	−	0.964559i	$-0.584998\pi$
$859$	−15.4672	−0.527736	−0.263868	+	0.964559i	$0.584998\pi$
$860$	−68.2489	−2.32727
$861$	−78.8494	−2.68718
$862$	20.6614	0.703730
$863$	−49.5601	−1.68705	−0.843524	−	0.537092i	$-0.819523\pi$
$863$	−49.5601	−1.68705	−0.843524	+	0.537092i	$0.819523\pi$
$864$	−44.9073	−1.52778
$865$	−73.6575	−2.50443
$866$	−15.3295	−0.520919
$867$	−37.8478	−1.28538
$868$	126.720	4.30117
$869$	−13.7787	−0.467411
$870$	69.8158	2.36698
$871$	72.7483	2.46498
$872$	−94.9601	−3.21576
$873$	13.7707	0.466068
$874$	−16.0659	−0.543437
$875$	15.1969	0.513751
$876$	87.6841	2.96257
$877$	3.87202	0.130749	0.0653745	−	0.997861i	$-0.479176\pi$
$877$	3.87202	0.130749	0.0653745	+	0.997861i	$0.479176\pi$
$878$	69.7354	2.35346
$879$	44.1314	1.48852
$880$	−97.2028	−3.27670
$881$	9.67844	0.326075	0.163037	−	0.986620i	$-0.447871\pi$
$881$	9.67844	0.326075	0.163037	+	0.986620i	$0.447871\pi$
$882$	−46.3109	−1.55937
$883$	−33.8578	−1.13941	−0.569703	−	0.821851i	$-0.692942\pi$
$883$	−33.8578	−1.13941	−0.569703	+	0.821851i	$0.692942\pi$
$884$	−45.9437	−1.54525
$885$	−91.2824	−3.06842
$886$	111.831	3.75705
$887$	−29.7254	−0.998080	−0.499040	−	0.866579i	$-0.666314\pi$
$887$	−29.7254	−0.998080	−0.499040	+	0.866579i	$0.666314\pi$
$888$	−29.4768	−0.989178
$889$	−21.1435	−0.709129
$890$	−90.6784	−3.03955
$891$	−11.6542	−0.390431
$892$	−144.942	−4.85303
$893$	−38.8553	−1.30024
$894$	63.5103	2.12410
$895$	−5.98144	−0.199937
$896$	114.070	3.81083
$897$	−13.9906	−0.467132
$898$	−83.8891	−2.79942
$899$	−20.1840	−0.673174
$900$	131.168	4.37226
$901$	10.9916	0.366184
$902$	−48.5088	−1.61517
$903$	−33.1199	−1.10216
$904$	47.5184	1.58044
$905$	−55.9978	−1.86143
$906$	−85.8618	−2.85257
$907$	8.92331	0.296294	0.148147	−	0.988965i	$-0.452669\pi$
$907$	8.92331	0.296294	0.148147	+	0.988965i	$0.452669\pi$
$908$	97.2497	3.22734
$909$	−13.1973	−0.437728
$910$	166.013	5.50327
$911$	47.3535	1.56889	0.784445	−	0.620198i	$-0.212948\pi$
$911$	47.3535	1.56889	0.784445	+	0.620198i	$0.212948\pi$
$912$	222.873	7.38005
$913$	−10.4439	−0.345643
$914$	−22.2381	−0.735570
$915$	58.7323	1.94163
$916$	−133.645	−4.41575
$917$	−34.2198	−1.13004
$918$	−9.33180	−0.307995
$919$	6.33157	0.208859	0.104430	−	0.994532i	$-0.466698\pi$
$919$	6.33157	0.208859	0.104430	+	0.994532i	$0.466698\pi$
$920$	31.2568	1.03051
$921$	51.7511	1.70526
$922$	109.306	3.59980
$923$	−6.24126	−0.205434
$924$	−95.5431	−3.14314
$925$	7.69676	0.253068
$926$	71.1455	2.33799
$927$	24.2889	0.797754
$928$	−60.5701	−1.98831
$929$	−13.7528	−0.451215	−0.225608	−	0.974218i	$-0.572437\pi$
$929$	−13.7528	−0.451215	−0.225608	+	0.974218i	$0.572437\pi$
$930$	−165.785	−5.43629
$931$	26.2331	0.859757
$932$	−89.5718	−2.93402
$933$	−12.6060	−0.412701
$934$	90.5229	2.96200
$935$	−10.6659	−0.348813
$936$	190.260	6.21885
$937$	32.3999	1.05846	0.529230	−	0.848478i	$-0.322481\pi$
$937$	32.3999	1.05846	0.529230	+	0.848478i	$0.322481\pi$
$938$	−125.125	−4.08547
$939$	−16.5922	−0.541466
$940$	119.924	3.91151
$941$	36.0722	1.17592	0.587960	−	0.808890i	$-0.299931\pi$
$941$	36.0722	1.17592	0.587960	+	0.808890i	$0.299931\pi$
$942$	33.0564	1.07704
$943$	8.92006	0.290477
$944$	149.975	4.88128
$945$	24.6191	0.800859
$946$	−20.3756	−0.662469
$947$	−12.2381	−0.397684	−0.198842	−	0.980032i	$-0.563718\pi$
$947$	−12.2381	−0.397684	−0.198842	+	0.980032i	$0.563718\pi$
$948$	−97.5089	−3.16694
$949$	−33.2100	−1.07804
$950$	−101.766	−3.30173
$951$	−43.2481	−1.40242
$952$	49.8114	1.61440
$953$	1.60774	0.0520799	0.0260400	−	0.999661i	$-0.491710\pi$
$953$	1.60774	0.0520799	0.0260400	+	0.999661i	$0.491710\pi$
$954$	−72.2107	−2.33791
$955$	−29.9336	−0.968629
$956$	1.46460	0.0473685
$957$	15.2181	0.491931
$958$	−5.52342	−0.178454
$959$	13.9396	0.450134
$960$	−243.228	−7.85013
$961$	16.9289	0.546092
$962$	17.7111	0.571030
$963$	35.0577	1.12972
$964$	−152.430	−4.90943
$965$	61.7258	1.98702
$966$	24.0633	0.774225
$967$	52.3837	1.68455	0.842274	−	0.539050i	$-0.181217\pi$
$967$	52.3837	1.68455	0.842274	+	0.539050i	$0.181217\pi$
$968$	65.0756	2.09161
$969$	24.4555	0.785625
$970$	32.9754	1.05878
$971$	30.7965	0.988307	0.494154	−	0.869375i	$-0.335478\pi$
$971$	30.7965	0.988307	0.494154	+	0.869375i	$0.335478\pi$
$972$	−117.560	−3.77074
$973$	−40.6971	−1.30469
$974$	−18.8504	−0.604004
$975$	−88.6204	−2.83812
$976$	−96.4960	−3.08876
$977$	7.57716	0.242415	0.121207	−	0.992627i	$-0.461323\pi$
$977$	7.57716	0.242415	0.121207	+	0.992627i	$0.461323\pi$
$978$	54.0531	1.72843
$979$	−19.7656	−0.631711
$980$	−80.9670	−2.58639
$981$	39.1455	1.24982
$982$	36.6277	1.16884
$983$	−61.9720	−1.97660	−0.988299	−	0.152526i	$-0.951259\pi$
$983$	−61.9720	−1.97660	−0.988299	+	0.152526i	$0.951259\pi$
$984$	−216.391	−6.89828
$985$	−24.2589	−0.772954
$986$	−12.5866	−0.400837
$987$	58.1971	1.85243
$988$	−170.975	−5.43944
$989$	3.74678	0.119141
$990$	70.0710	2.22700
$991$	−47.3471	−1.50403	−0.752015	−	0.659146i	$-0.770918\pi$
$991$	−47.3471	−1.50403	−0.752015	+	0.659146i	$0.770918\pi$
$992$	143.830	4.56660
$993$	−86.2269	−2.73633
$994$	10.7348	0.340486
$995$	−90.9189	−2.88232
$996$	−73.9092	−2.34190
$997$	−54.4034	−1.72297	−0.861487	−	0.507780i	$-0.830466\pi$
$997$	−54.4034	−1.72297	−0.861487	+	0.507780i	$0.830466\pi$
$998$	1.88931	0.0598051
$999$	2.62650	0.0830987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.3	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.3	✓	143	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72223 q^{2} +2.61290 q^{3} +5.41054 q^{4} -3.36664 q^{5} -7.11292 q^{6} -3.38304 q^{7} -9.28427 q^{8} +3.82726 q^{9} +O(q^{10})\)	\(q-2.72223 q^{2} +2.61290 q^{3} +5.41054 q^{4} -3.36664 q^{5} -7.11292 q^{6} -3.38304 q^{7} -9.28427 q^{8} +3.82726 q^{9} +9.16478 q^{10} +1.99769 q^{11} +14.1372 q^{12} -5.35442 q^{13} +9.20942 q^{14} -8.79672 q^{15} +14.4528 q^{16} +1.58589 q^{17} -10.4187 q^{18} +5.90174 q^{19} -18.2154 q^{20} -8.83957 q^{21} -5.43817 q^{22} +1.00000 q^{23} -24.2589 q^{24} +6.33429 q^{25} +14.5760 q^{26} +2.16156 q^{27} -18.3041 q^{28} +2.91547 q^{29} +23.9467 q^{30} -6.92307 q^{31} -20.7754 q^{32} +5.21977 q^{33} -4.31716 q^{34} +11.3895 q^{35} +20.7076 q^{36} +1.21509 q^{37} -16.0659 q^{38} -13.9906 q^{39} +31.2568 q^{40} +8.92006 q^{41} +24.0633 q^{42} +3.74678 q^{43} +10.8086 q^{44} -12.8850 q^{45} -2.72223 q^{46} -6.58370 q^{47} +37.7639 q^{48} +4.44498 q^{49} -17.2434 q^{50} +4.14378 q^{51} -28.9703 q^{52} +6.93088 q^{53} -5.88426 q^{54} -6.72551 q^{55} +31.4091 q^{56} +15.4207 q^{57} -7.93658 q^{58} +10.3769 q^{59} -47.5950 q^{60} -6.67661 q^{61} +18.8462 q^{62} -12.9478 q^{63} +27.6498 q^{64} +18.0264 q^{65} -14.2094 q^{66} -13.5866 q^{67} +8.58053 q^{68} +2.61290 q^{69} -31.0049 q^{70} +1.16563 q^{71} -35.5333 q^{72} +6.20236 q^{73} -3.30776 q^{74} +16.5509 q^{75} +31.9316 q^{76} -6.75827 q^{77} +38.0856 q^{78} -6.89733 q^{79} -48.6576 q^{80} -5.83385 q^{81} -24.2825 q^{82} -5.22799 q^{83} -47.8268 q^{84} -5.33913 q^{85} -10.1996 q^{86} +7.61784 q^{87} -18.5471 q^{88} -9.89423 q^{89} +35.0760 q^{90} +18.1142 q^{91} +5.41054 q^{92} -18.0893 q^{93} +17.9224 q^{94} -19.8691 q^{95} -54.2842 q^{96} +3.59806 q^{97} -12.1003 q^{98} +7.64569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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